Theorem pm3.31 445

Description: Theorem *3.31 (Imp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)

Assertion

Ref	Expression
pm3.31	|- ( ( ph -> ( ps -> ch ) ) -> ( ( ph /\ ps ) -> ch ) )

Proof of Theorem pm3.31

Step	Hyp	Ref	Expression
1		id 22	. 2 |- ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( ps -> ch ) ) )
2	1	impd 431	1 |- ( ( ph -> ( ps -> ch ) ) -> ( ( ph /\ ps ) -> ch ) )

Syntax hints:   -> wi 4   /\ wa 369

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 185  df-an 371

This theorem is referenced by:  impexp  446  imp5a  598  issref  5320  stoweidlem17  29961  trsbc  31580  3impexpVD  31925  trsbcVD  31946  19.41rgVD  31971